求解二维不可压缩Navier-Stokes方程的混合型微分求积法  被引量:3

A Mixture Differential Quadrature Method for Solving Two-Dimensional Incompressible Navier-Stokes Equations

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作  者:孙建安[1] 朱正佑[2] 

机构地区:[1]西北师范大学物理系,兰州730070 [2]上海大学数学系上海市应用数学和力学研究所,上海200072

出  处:《应用数学和力学》1999年第12期1259-1266,共8页Applied Mathematics and Mechanics

摘  要:微分求积法(DQM)能以较少的网格点求得微分方程的高精度数值解,但采用单纯的微分求积法求解二维不可压缩Navier_Stokes 方程时,只能对低雷诺数流动获得较好的数值解,当雷诺数较高时会导致数值解不收敛· 为此,提出了一种微分求积法与迎风差分法混合求解二维不可压缩Navier_Stokes 方程的预估_校正数值格式,用伪时间相关算法以较少的网格点获得了较高雷诺数流动的数值解· 作为算例,对1∶1 和1∶2 驱动方腔内的流动进行了计算,得到了较好的数值结果·Differential quadrature method (DQM) is able to obtain highly accurate numerical solutions of differential equations just using a few grid points. But using purely differential quadrature method, good numerical solutions of two_dimensional incompressible Navier_Stokes equations can be obtained only for low Reynolds number flow and numerical solutions will not be convergent for high Reynolds number flow. For this reason, in this paper a combinative predicting_correcting numerical scheme for solving two_dimensional incompressible Navier_Stokes equations is presented by mixing upwind difference method into differential quadrature one. Using this scheme and pseudo_time_dependent algorithm, numerical solutions of high Reynolds number flow are obtained with only a few grid points. For example, 1∶1 and 1∶2 driven cavity flows are calculated and good numerical solutions are obtained.

关 键 词:数值方法 微分求积法 不可压缩流体 N-S方程 

分 类 号:O357.1[理学—流体力学] O241.82[理学—力学]

 

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